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A method for combining inference across related nonparametric Bayesian models

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  • Peter Müller
  • Fernando Quintana
  • Gary Rosner

Abstract

Summary. We consider the problem of combining inference in related nonparametric Bayes models. Analogous to parametric hierarchical models, the hierarchical extension formalizes borrowing strength across the related submodels. In the nonparametric context, modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional. We discuss a formal definition of such a hierarchical model. The approach includes a regression at the level of the nonparametric model. For the special case of Dirichlet process mixtures, we develop a Markov chain Monte Carlo scheme to allow efficient implementation of full posterior inference in the given model.

Suggested Citation

  • Peter Müller & Fernando Quintana & Gary Rosner, 2004. "A method for combining inference across related nonparametric Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 735-749, August.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:3:p:735-749
    DOI: 10.1111/j.1467-9868.2004.05564.x
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    Cited by:

    1. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
    2. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    3. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    4. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    5. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    6. Hatjispyros, Spyridon J. & Merkatas, Christos & Nicoleris, Theodoros & Walker, Stephen G., 2018. "Dependent mixtures of geometric weights priors," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 1-18.
    7. George Karabatsos & Stephen Walker, 2009. "A Bayesian Nonparametric Approach to Test Equating," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 211-232, June.
    8. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    9. Abel Rodr�guez & Enrique ter Horst, 2011. "Measuring expectations in options markets: an application to the S&P500 index," Quantitative Finance, Taylor & Francis Journals, vol. 11(9), pages 1393-1405, July.
    10. Marta Catalano & Claudio Del Sole & Antonio Lijoi & Igor Prünster, 2024. "A Unified Approach to Hierarchical Random Measures," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 255-287, November.
    11. Monica Billio & Roberto Casarin & Luca Rossini, 2016. "Bayesian nonparametric sparse seemingly unrelated regression model (SUR)," Working Papers 2016:20, Department of Economics, University of Venice "Ca' Foscari".
    12. repec:jss:jstsof:40:i05 is not listed on IDEAS
    13. Rodrigues, G.S. & Nott, David J. & Sisson, S.A., 2016. "Functional regression approximate Bayesian computation for Gaussian process density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 229-241.
    14. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Antonio Lijoi & Bernardo Nipoti & Igor Prünster, 2013. "Dependent mixture models: clustering and borrowing information," DEM Working Papers Series 046, University of Pavia, Department of Economics and Management.
    16. Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2014. "Dependent mixture models: Clustering and borrowing information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 417-433.
    17. Mahsa Samsami & Ralf Wagner, 2021. "Investment Decisions with Endogeneity: A Dirichlet Tree Analysis," JRFM, MDPI, vol. 14(7), pages 1-19, July.
    18. Andrew Cron & Cécile Gouttefangeas & Jacob Frelinger & Lin Lin & Satwinder K Singh & Cedrik M Britten & Marij J P Welters & Sjoerd H van der Burg & Mike West & Cliburn Chan, 2013. "Hierarchical Modeling for Rare Event Detection and Cell Subset Alignment across Flow Cytometry Samples," PLOS Computational Biology, Public Library of Science, vol. 9(7), pages 1-14, July.

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